Much of the original content (quests, dungeons, raids, etc.) from each of those old expansions is still available and is still playable. Some exceptions exist; for example, the level 60 version of Naxxramas from version 1.11 is no longer accessible within the game, since it was replaced with the Northrend version in Wrath of the Lich King. Many old quests, NPCs, and zones were removed or redesigned completely when Azeroth was reshaped for Cataclysm. Some things have endured unchanged since their implementation, however (such as most of the Outland content) and that content is mostly still perfectly accessible.
However, wide system-level changes have occurred to the game many times over in the intervening time, and those changes apply to all players, regardless of their level or what expansions they own. For example, the talent system has been redesigned several times over the lifespan of the game, and all characters are subject to the latest version of that system; it's impossible to play the game today using the talent system from an earlier period in time. Similarly, more recent feature additions such as pet battles, achievements, and the dungeon finder are accessible to all characters.
As far as "what content can I play with which expansions," you need to own every expansion in order to level up to the maximum level cap. It is not possible to play through all of the previous content all the way up to the current level cap simply by buying Mists of Pandaria and skipping all previous expansions. (Since the base game now automatically includes all expansions up through Mists of Pandaria, though, this point is largely moot.)